1. Field of the Invention
The invention relates to a method of correcting a complex resonance spectrum obtained from sampling values of at least one resonance signal by Fourier transformation, which resonance signals are generated by means of R.F. electromagnetic pulses in an object situated in a steady, uniform magnetic field, there being determined peak locations in the complex spectrum and phase values in the peak locations.
The invention also relates to a device for determining a complex magnetic resonance spectrum of at least a part of an object, which device comprises means for generating a steady magnetic field, means for applying magnetic field gradients on the steady, uniform magnetic field, means for transmitting R.F. electromagnetic pulses in order to excite resonance signals in the object, means for receiving and detecting the excited resonance signals and means for generating sampling values from the detected resonance signals, and also comprises programmed means for determining, using Fourier transformation, the complex magnetic resonance spectrum from the sampling values, which programmed means are also suitable for determining peak locations in the complex spectrum and phase values in the peak locations.
2. Description of the Prior Art
A method of this kind is known from the article by C. H. Sotak et al. in "Journal of Magnetic Resonance", Vol. 57, pp. 453-462, 1984. Said article describes a non-iterative automatic phase correction for a complex magnetic resonance spectrum containing phase errors. The phase errors are due inter alia to deficiencies of the NMR device, for example misadjustment of the means for receiving and detecting the resonance signals or the finite width of the R.F. electromagnetic pulses; phase errors occur notably also due to incorrect timing. For example, when the resonance signal (the so-called FID signal) which occurs immediately after the R.F. electromagnetic pulse is sampled, in practice the instant at which the FID signal commences will hardly ever coincide with the instant at which a first sampling value is obtained. Across the complex spectrum, therefore, frequency-independent (zero-order) as well as frequency-dependent (first order and higher order) phase errors will occur. In said article a method is proposed for correcting zero-order and first-order phase errors by way of a linear phase correction across the complex spectrum. The complex spectrum can be considered to be a real and an imaginary spectrum (absorption mode and dispersion mode, respectively). Using a so-called DISPA (plot of dispersion versus absorption), an image is indicated for a single Lorentzian spectral line. When the Lorentzian spectral line is ideal (i.e. when there is no phase shift), an image is produced in the form of a circle which serves as a reference image for non-ideal Lorentzian lines. Using a DISPA, in principle the phase error of non-ideal Lorentzian lines can be determined with respect to an ideal Lorentzian line. The linear phase correction disclosed in the cited article utilizes this phenomenon in order to determine the frequency-dependent phase error. First a power spectrum is determined from the complex spectrum and peak locations of suitable resonance lines are determined from said power spectrum. Subsequently, the phase of a peak nearest to the centre of the spectrum is determined by means of DISPA. Using this phase, the zero-order phase error is corrected. Subsequently, the phase of the other peaks is determined by means of DISPA and, using the phases of the other peaks determined, a linear phase variation is estimated as well as possible in order to approximate the first-order phase error. Using the approximation found for the zero-order and first-order phase error, the complex spectrum is ultimately phase-corrected point by point. The known method imposes requirements as regards peak separation; peaks in the spectrum which are comparatively near to one another cannot be used. Furthermore, there must be at least two peaks which are comparatively remote from one another in the spectrum; if this is not the case, it will be necessary to create two remote peaks in the spectrum by the addition of an agent. By using linear phase correction in the known method, for example only phase shifts will be compensated for which are caused by the time shifted measurement of the resonance signals. Inevitably present phase errors due to other causes, will not be covered.
It is an object of the invention to provide a method which does not have the described drawbacks.
To achieve this, a method in accordance with the invention is characterized in that coefficients of a frequency-dependent phase function extending across the complex spectrum are approximated from the phase values in the peak locations in accordance with a predetermined criterion, after which the complex spectrum is corrected by means of the frequency-dependent phase function determined. The frequency-dependent phase function may be a polynomial whose degree may be predetermined. It is alternatively possible to define the power of the polynomial during the approximation. As a result, any phase-dependency can be approximated. The method in accordance with the invention is based on the recognition of the fact that the phases in the peak locations of the complex spectrum must be zero in the absence of phase errors; the absorption mode signal is then maximum and the dispersion mode signal is zero. When the coefficients of the frequency-dependent phase function have been determined, the complex spectrum can be corrected by means of the frequency-dependent phase function determined by point-wise correcting the real and the imaginary part thereof as a function of the frequency.
A version of a method in accordance with the invention is characterized in that the peak locations are derived from a modulus spectrum which is determined from the complex spectrum. The peak locations can be suitably determined from the modulus spectrum because this spectrum is not influenced by the phase errors occurring.
A version of a method in accordance with the invention in which peak parameters are determined in the peak locations during the determination of the peak locations is characterized in that in the case of overlapping peaks the overlapping peaks are corrected by means of the peak parameters determined. The peak parameters determined for overlapping peaks can be used for correcting neighbouring overlapping peaks by utilizing the fact that the real and the imaginary part must satisfy Lorentzian formulas; an excessive contribution to a line can be subtracted from a neighbouring line. If such a correction were not performed, ultimately a spectrum which has not been completely corrected could be obtained. It is to be noted that such a correction can be dispensed with in the case of spectra comprising numerous lines. When a wide background is present in the spectrum, the parameters of the wide background (which may be considered to be a wide spectral line) can be determined; using the method described for correcting overlapping lines, the parameters determined for the wide background can be used to eliminate the effect of the wide background.
Moreover, a model of the complex spectrum can be calculated on the basis of the peak locations and peak parameters determined. The phase of the complex spectrum can then be corrected in the peak locations by means of the frequency-dependent phase function determined and in frequencies outside the peak locations by means of a weighted phase from the phases of the peak locations. Using the model, the degree of contribution of the peaks to a frequency outside the peak locations is determined in order to determine weighting factors for the weighted phase. Notably when a very strong peak is present in the spectrum, for example a water peak in proton spectra, it may be necessary to use such a somewhat refined correction.
The invention will be described in detail hereinafter whith reference to a drawing; therein: